comonad: Comonads

[ bsd3, comonads, control, library ] [ Propose Tags ]


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Versions [faq] 0.1.0, 0.1.1, 0.3.0, 0.4.0, 0.5.0, 0.6.0, 0.6.1,,, 0.6.2,, 0.7.0, 0.9.0,, 1.0, 1.0.1, 1.0.2, 1.0.3, 1.1.0,,, 1.1.1,,,,,,, 3.0,,,, 3.0.2, 3.0.3, 3.1, 4.0, 4.0.1, 4.2, 4.2.1, 4.2.2, 4.2.3, 4.2.4, 4.2.5, 4.2.6, 4.2.7,,, 4.3, 5, 5.0.1, 5.0.2, 5.0.3, 5.0.4, 5.0.5, 5.0.6, 5.0.7, 5.0.8
Change log CHANGELOG.markdown
Dependencies base (==4.*), containers (>=0.3 && <0.7), distributive (>=0.2.2 && <1), semigroups (>=0.16.2 && <1), tagged (>=0.7 && <1), transformers (>=0.2 && <0.6), transformers-compat (>=0.3 && <1) [details]
License BSD-3-Clause
Copyright Copyright (C) 2008-2014 Edward A. Kmett, Copyright (C) 2004-2008 Dave Menendez
Author Edward A. Kmett
Maintainer Edward A. Kmett <>
Category Control, Comonads
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Source repo head: git clone git://
Uploaded by ryanglscott at 2019-05-02T17:25:53Z
Distributions Arch:5.0.8, Debian:5.0.4, Fedora:5.0.6, FreeBSD:, LTSHaskell:5.0.5, NixOS:5.0.8, Stackage:5.0.5, openSUSE:5.0.6
Downloads 260541 total (2014 in the last 30 days)
Rating 2.5 (votes: 5) [estimated by Bayesian average]
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Status Hackage Matrix CI
Docs available [build log]
Last success reported on 2019-05-02 [all 1 reports]


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Readme for comonad-5.0.5

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This package provides comonads, the categorical dual of monads. The typeclass provides three methods: extract, duplicate, and extend.

class Functor w => Comonad w where
    extract :: w a -> a
    duplicate :: w a -> w (w a)
    extend :: (w a -> b) -> w a -> w b

There are two ways to define a comonad:

I. Provide definitions for extract and extend satisfying these laws:

extend extract      = id
extract . extend f  = f
extend f . extend g = extend (f . extend g)

In this case, you may simply set fmap = liftW.

These laws are directly analogous to the laws for monads. The comonad laws can perhaps be made clearer by viewing them as stating that Cokleisli composition must be a) associative and b) have extract for a unit:

f =>= extract   = f
extract =>= f   = f
(f =>= g) =>= h = f =>= (g =>= h)

II. Alternately, you may choose to provide definitions for fmap, extract, and duplicate satisfying these laws:

extract . duplicate      = id
fmap extract . duplicate = id
duplicate . duplicate    = fmap duplicate . duplicate

In this case, you may not rely on the ability to define fmap in terms of liftW.

You may, of course, choose to define both duplicate and extend. In that case, you must also satisfy these laws:

extend f  = fmap f . duplicate
duplicate = extend id
fmap f    = extend (f . extract)

These implementations are the default definitions of extend andduplicate and the definition of liftW respectively.

Contact Information

Contributions and bug reports are welcome!

Please feel free to contact me through github or on the #haskell IRC channel on

-Edward Kmett